Table 4 Quantitative synthesis methods

Bayesian synthesis [53]

To measure the likelihood of different values for parameters of interest.

Incorporates prior distributions of unknown parameter values that are then updated by deriving posterior probability distributions generated through statistical analysis of the estimates.

Case survey [54, 55]

To identify and statistically test patterns across individual case studies.

Converts qualitative cases into quantitative variables by extracting data using a same set of closed-ended questions. The answers to these questions are then aggregated to establish frequency of occurrence (that can be further statistically analyzed, as appropriate).

Configurational comparative method [56]

To build or test theories and assumptions by identifying configurations of causal conditions, i.e., combination of conditions (independent variables) that are necessary and/or sufficient for a given outcome (dependent variable).

Consists in a comparative case-oriented research approach that uses Boolean algebra to generate configurations between conditions and outcomes across cases.

Cross-design synthesis [57]

To combine results from quantitative studies with complementary designs (e.g., RCT and observational studies).

Involves an in-depth assessment of key biases of each study, an adjustment of each study’s results based on the identified biases and the development of a model for combining the results within and across designs.

Meta-analysis [58]

To obtain a single summarized “effect size.”

Uses statistical methods for combining results of studies into a weighted average of point estimates.

Meta-regression [59]

To relate the size of effect to one or more characteristics of the included studies (to explore sources of heterogeneity across included studies).

Uses a combination of meta-analytic and regression principles.

Meta-summary [60]

To quantitatively aggregate qualitative findings.

Consists of extraction, grouping, abstraction, and formatting of findings and the calculation of frequency and intensity effect sizes.

Quantitative content analysis [27, 28]

To transform qualitative data into few variables (numerical value) for statistical analysis.

Categorizes data and provides statistical description of the categories.

Vote counting [61]

To calculate the frequencies of categories of results across included studies.

The included studies are sorted into three categories (negative significant, positive significant, and statistically insignificant), and the number of studies for each category is calculated. The category with the most studies is the “winner.”